course: "Eulerian polynomials, lattice points counting, and arrangements."
speaker: Masahiko Yoshinaga (Hokkaido University, Sapporo)abstract: One of the most important combinatorial invariant of an arrangement is the so-called characteristic polynomial. Recently, Kamiya-Takemura-Terao introduced the notion of "characteristic quasi-polynomial" which is a refinement of characteristic polynomials, and has close relationships with Ehrhart quasi-polynomials of rational polytopes. In this course, I would explain these materials together with Eulerian polynomials and then apply to "Riemann hypothesis for Linial arrangements" by Postnikov-Stanley.
(Reference: arXiv:1501.04955 and references in it.)
Contents:
1. Characteristic quasi-polynomials of integral arrangements (due to
Kamiya-Takemura-Terao).
2. Ehrhart theory. (Ehrhart quasi-polynomials for rational polytopes.)
3. Eulerian polynomials and root system generalizations (along the work by Lam-Postnikov).
4. Location of zeros of characteristic polynomials.
timetable:
Wed 31 Aug, 14:30 - 16:30, Aula Dini
Thu 1 Sep, 14:30 - 16:30, Aula Dini
Fri 2 Sep, 8:30 - 10:30, Aula Dini
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